According to the discriminant of the quadratic equation, it will have equal roots for p = -16.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
If [tex]\mathbf{\Delta > 0}[/tex], and it is a perfect square, it has 2 rational solutions.If [tex]\mathbf{\Delta > 0}[/tex], and it is not a perfect square, it has 2 irrational solutions.If [tex]\mathbf{\Delta = 0}[/tex], it has equal roots.If [tex]\mathbf{\Delta < 0}[/tex], it has 2 complex solutions.In this problem, the equation is:
[tex]f(x) = -x^2 + 8x + p[/tex]
Hence the coefficients are a = -1, b = 8, c = p.
It has equal roots if [tex]\Delta = 0[/tex], hence:
[tex]b^2 - 4ac = 0[/tex]
[tex]8^2 + 4p = 0[/tex]
[tex]4p = -64[/tex]
[tex]p = -16[/tex]
More can be learned about the discriminant of a quadratic equation at https://brainly.com/question/19776811
please PLEASE PLEASE
14, 21
Step-by-step explanation:
Let the two consecutive multiples be 7n and 7(n+1).
Now, it is given that:
(7n)² + [7(n+1)]² = 637
Simplifying,
49n² + (7n+7)² = 637
49n² + 49n² + 2(7n)(7) + 49 = 637
(as (x+y)² = x² + y² + 2xy)
98n² + 98n + 49 = 637
98n² + 98n - 588 = 0
Dividing by 98 to further simplify,
n² + n - 6 = 0
Factorising, we get
n² + 3n - 2n - 6 = 0
n(n+3) - 2(n+3) = 0
(n+3)(n-2) = 0
Therefore we get n = -3 or n = +2.
Hence, we get the consecutive multiples as 14 and 21.
Feel free to ask if you didn't understand any part.
Hope this helps! :D
Given that
[tex]2 {}^{x} = 0.125[/tex]
Find x
Answer:
x = -3.
Step-by-step explanation:
2^x = 0.125
Taking logs:
x ln 2 = ln 0.125
x = ln 0.125 / ln 2
x = -3
-4x+y=6 -5x-y=21 solve by substiution
Answer:
55
Step-by-step explanation:
55 is your answer
Answer:
Step-by-step explanation:
Subtract
2
y
from both sides of the equation.
x
=
12
−
2
y
−
x
=
−
y
−
6
Replace all occurrences of
x
with
12
−
2
y
in each equation.
Tap for more steps...
−
12
+
2
y
=
−
y
−
6
x
=
12
−
2
y
Solve for
y
in the first equation.
Tap for more steps...
y
=
2
x
=
12
−
2
y
Replace all occurrences of
y
with
2
in each equation.
Tap for more steps...
x
=
8
y
=
2
The solution to the system is the complete set of ordered pairs that are valid solutions.
(
8
,
2
)
The result can be shown in multiple forms.
Point Form:
(
8
,
2
)
Equation Form:
x
=
8
,
y
=
2
What statement about the volume of the cylinder and cone is true ?
Answer:c
Step-by-step explanation:
A hose fills a 10,000-gallon swimming pool at a rate of 10 gallons per minute. what is the domain and range?
Answer:
Domain: 0 minutes to time it takes to fill. Range: 0 to a 10,000 gallons
Step-by-step explanation:
The domain will be from 0 minutes to time it takes to fill i.e., 1000 and range will be from 0 to 10000 gallons.
It is given that a hose fills 10000 gallon swimming pool at rate of 10 gallons per minute.
We have to find the domain and range.
What do you mean by domain and range ?
The domain is the set of all values for which the function is defined and the range of the function is the set of all values that function takes.
As per the question ;
Capacity of swimming pool = 10000 gallons
Rate of filling = 10 gallons per minute
So ;
Time taken in filling the swimming pool will be ;
= 10000 / 10
= 1000 minutes
So ;
The domain will be from 0 to 1000 minutes i.e., time taken to fill the swimming pool.
Whereas ;
The range will be from 0 to 10000 gallons i.e., amount of swimming pool filled.
Thus , the domain will be from 0 minutes to time it takes to fill i.e., 1000 and range will be from 0 to 10000 gallons.
To learn more about domain and ranges click here ;
https://brainly.com/question/26098895
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please help marking u Brainiest if answered
Simplify the expression.
4x^2 + 10x - 6
———————
2x-1
-X+ 5
X+3
2(x + 3)
2x-6
2. If the hovercraft is traveling in a straight line at a constant speed of 8 m/s for 4 seconds, what is it's
acceleration?
Answer:
Step-by-step explanation:
a= v/t, where v is the speed and t is the time
a=8/4= 2 m/s^2
*I NEED THIS DONE TONIGHT*
If you have a 4 gallon bucket and a 9 gallon bucket, how do you get 2 gallons if you have NO other containers and you can NOT estimate (ex: dump about 1 gallon out)
Answer:
how you do it is you pour 4 gallions into the 9 gallon bucket then fill the 4 gallon bucket up halfway to get your two gallons
Step-by-step explanation:
Factored completely, the expression 2x^2+10x-12 is equivalent to:
Answer:
(x + 6) (x - 1)
Step-by-step explanation:
2x² + 10x - 12
dividing by 2,
x² + 5x - 6
x² - x + 6x - 6
x(x - 1) + 6(x - 1)
(x + 6) (x - 1)
x = -6 or x = 1
Simplify ech answer into a fraction, Show all work please!
Answer:
the first one is -9/40. the second one is 109/20. the third one is -8/35.
Step-by-step explanation:
here is the work for the first one 3/8-.6 and convert into a simplified fraction and came up with -9/40. here is the work for the second one 4 4/3+0.7 and then convert into a simplified fraction and came up with 109/20. here is the work for the third one 4/7-0.8 and then convert into a simplified fraction and came up with -8/35.
Fund the value of x! I need this asap!! Please dont get it wrong and first correct answer gets brainliest!!
Answer:
Step-by-step explanation:
What is the equation???
1⁄4 + 4⁄8 + 4⁄6 = ???
☁️ Answer ☁️
Exact form:
17/12
Decimal:
1.416
mixed:
1 5/12
Hope it helps.
Have a nice day hyung/noona ￣▽￣
Write the expression in standard form: 5(3a) + 8(-5b) + (4 * c * 6) * = Multiplication symbol
Answer:
use photomath and your welcome :)))
Two rectangles are similar. If the helght of the first rectangle is 3 Inches, and the helght of the second rectangle is 9 Inches, how much larger is the second rectangle's area?
1. They have the same area
2. 9 times as large
3. 3 times as large
4. 6 times as large
Answer:
3
Step-by-step explanation:
A cast member is selling balloons on Main Street. He has 8
princess balloons, 5 blue Mickey balloons, and 7 red Mickey
balloons. He sells one balloon, and then another (no replacing).
Find the probability of selling one blue balloon followed by
another blue balloon and show the equation used.
Answer:
4/76 or simplified as 1/19
Step-by-step explanation:
5/20 is for the probability of the first balloon
4/19 is for the probability of the second balloon
5/20 can be simplified to 1/4 so 1/4 x 4/19 = 4/76
4/76 can also be simplified to 1/19
What is the equation of the line that passes through the point (-6,7) and has a slope of -5? Write the equation in slope intercept form
Answer:
asap
Step-by-step explanation:
i will do it asap ...hejei
A
∠A and
∠
B
∠B are vertical angles. If m
∠
A
=
(
5
x
−
24
)
∘
∠A=(5x−24)
∘
and m
∠
B
=
(
3
x
+
24
)
∘
∠B=(3x+24)
∘
, then find the value of x.
Answer:
24 degrees
Step-by-step explanation:
Which rule explains why these triangles are congruent?
Answer:
ASA
Step-by-step explanation:
ANGLE SIDE ANGLE
according to your option
find the value of x plz help <3
Suppose Rachel creates 1.5 pounds of trash each week. How many kilograms of trash is that? Choose the closest answer.
Answer:
.68
Step-by-step explanation:
mai is solving the equation (x-5)=0, she writes that the solutions are x=5 and x=-5. Han looks at her work and disagrees. he says that only x=5 is a solution. who do you agree with? explain your reasoning.
Answer:
Hey there, im assuming the parenthesis are absolute Value
Han is correct!
Step-by-step explanation:
|x-5|=0
possible solution are the opposite of -5, which is 5
|5-5|=0 (true)
If it was -5,
|-5-5|≠0, it equals 10
A. 118 degrees
B. 180 degrees
C. 64 degrees
D. 62 degrees
Will you brainliest for the correct answer!!!
Please help!!
Answer:
62 degrees
Step-by-step explanation:
you need to understand the def.ang.biscectors, it is going to mean if a life bisects another line, the two angles on one side will add up to 180
therefore
180-118=62
does 13, 12, 6 form a pythagorean triple?
Answer:
No
Step-by-step explanation:
the pythagorean theorem is
a^2+b^2=c^2
These numbers do not fit in these terms
Answer:
It doesn't.
Step-by-step explanation:
In order for something to be a {ythagorean triple, it must comply with the Pythagorean theorem, which is a² + b² = c²
Always remember, when plugging in the values into that equation, the exponent of two means to square the number, and a and b have to be the two smallest values (in this case, 6 and 12)
6² = 36
12² = 144
36 + 144 = 180
Now, we have to find if ti equals c². 13² equals 169
Therefore, 180 ≠ 169, therefore it IS NOT a Pythagorean triple.
which of the following is a function
Answer:
This question is incomplete since you did not provide the options needed. Anyway, I will give you an explanation that will be useful for you to understand this.
Step-by-step explanation:
Understanding what a function is will allow you to have more clarity when solving the functions exercises and you will be prepared to understand more concepts that surround functions such as domain, image, relative extremes, their representation on the axes, etc.
A function is a relationship between two variables, one independent (x) and the other dependent (y) and for each value of x there corresponds ONE SINGLE VALUE OF y.
For example :
f(x) = 3x2 + 1
2
Help what is the product of 46x10
Answer:
460
Step-by-step explanation:
Answer:
460
Step-by-step explanation:
What steps do you need to take to solve the equation 7x+6= 18?
*x
Choose the correct answer below.
A. Subtract 6. Then, multiply by 2.
B. Add 6. Then, multiply by 2.
C. Subtract 6. Then, divide by 2.
D. Add 6. Then, divide by 2.
1.) If ABCD is a parallelogram, which statement is true?
(1) AC = BD
(2) AD=BC
(3) ZA and ZC are supplementary
(4) ZA ZD
Answer:
think its two cuz i found a shape that matches ur questions
I need help to find the perimeter of this shape can somebody help me RN.
Which graph represents y as a function of x?
Answer:
A is the only function because it passes the vertical line test. 1 x may only have 1 y
Step-by-step explanation: